Q4. (i) m & n are two integers such that m=n2-n. Show that m2-2m is divisible by 24.
(ii) If x & y are two positive numbers such that x + y = 1, find maximum value of x4y + xy4.
(i) m = n2-n (Given)
So, m2 – 2m = n2(n-1)2 - 2n(n-1)
= n(n-1)[ n2 – n – 2]
=(n-2)(n-1)n(n+1) … Product of 4 consecutive integers
We know that product of any four consecutive integer is divisible by 4 !
Thus, m2-2m is divisible by 24.
(ii) solution is : HERE